Answer :
The resistance of a wire with a 1.6 mm diameter and 20 m length made of the same material is 3.14×10⁻⁷Ω−m.
What does "resistance" mean?
Electrical resistance of a conductor with a unit cross-sectional area and unit length is called resistivity. Resistivity is a distinctive attribute of any material that may be used to compare different materials based on how well they conduct electric currents. Low conductivity is indicated by high resistance.
Given,
l= 10m= 1000mm
d= 2mm
∴radius(r)= 20.2 =0.1mm
R=10Ω
To find,
Resistivity(ρ)
ρ=R /l A
where,
R= Resistance
l= Length of wire
A= Cross sectional area of wire
Cross sectional area of cylinder (A)=Πr²
A= π×(0.1)²
A=0.0314mm²
ρ=10(10000.0341)
ρ=0.000314Ω−mm
ρ≃3.14×10⁻⁷Ω−m
So, the resistivity of the material is equal to 3.14×10⁻⁷Ω−m.
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